A Posteriori Error Control for the Allen–Cahn Equation with Variable Mobility

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-07-17 DOI:10.1137/24m1646406

A. Brunk, J. Giesselmann, M. Lukáčová-Medvi[math]ová

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1540-1560, August 2025.
Abstract. In this work, we derive a [math]-robust a posteriori error estimator for finite element approximations of the Allen–Cahn equation with variable nondegenerate mobility. The estimator utilizes spectral estimates for the linearized steady part of the differential operator as well as a conditional stability estimate based on a weighted sum of Bregman distances, based on the energy and a functional related to the mobility. A suitable reconstruction of the numerical solution in the stability estimate leads to a fully computable estimator.

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变迁移率Allen-Cahn方程的后验误差控制

SIAM数值分析杂志，第63卷，第4期，第1540-1560页，2025年8月。摘要。在这项工作中，我们为具有可变非退化迁移率的Allen-Cahn方程的有限元近似导出了一个[数学]鲁棒的后检误差估计。该估计器利用微分算子线性化稳定部分的谱估计，以及基于布雷格曼距离加权和的条件稳定性估计，基于能量和与迁移率相关的函数。对稳定性估计中的数值解进行适当的重构，得到一个完全可计算的估计量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.